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Information and Entropy Econometrics
– Theory and Practice
Instructor: Amos
Golan, American University
DATES: MAY 16-20, 2005
LOCATION: AMERICAN UNIVERSITY
Objectives and Scope
Information and Entropy Econometrics (IEE) represents a class
of methods (within econometrics and statistics) that directly
or indirectly builds on the foundations of Information Theory
(IT) and the principle of Maximum Entropy (ME). IEE includes research
dealing with statistical inference of problems given incomplete
knowledge or data, as well as research dealing with the analysis,
diagnostics and statistical properties of information measures.
A common thread connecting all the IEE estimation methods is the
objective of trying to better understand the data, while abstracting
away from distributional assumptions or assumptions on the likelihood
function.
This class of methods includes the Bayesian Method of Moments
(BMOM), the Empirical (or Generalized Empirical) Likelihood (EL/GEL),
variations of the Generalized Method of Moments (GMM) and the
Generalized ME (GME). All of these methods share the same basic
objective of analyzing limited and noisy data using minimal assumptions.
Within the class of IEE methods, the GME is a robust estimation
method that is used, primarily, for analyzing finite or limited
data sets as well as data sets that are ill-conditioned or ill-behaved.
Most economic data fall within these types of ill-behaved data.
However, there are many other areas of scientific research where
this approach proves to be very useful. Like other IEE methods,
the GME uses minimum statistical (distributional) assumptions,
performs well under a large class of distributions and is easy
to apply and compute.
The primary purpose of this class is to provide the background
for understanding both (i) the theory, and (ii) to develop the
necessary theoretical and empirical tools for practicing the theory
in a wide range of economic/econometric estimation problems. Throughout
the course, entropy estimators will be compared with their traditional
counterparts and the computational aspects will be discussed and
practiced with artificial and real data (your ‘own’
dataset).
Preliminary time schedule
Monday May 16
09.00 - 12.00: Theory
1.00 - 4.30: Computer Lab
Tuesday May 17
09.00 - 12.00: Theory
1.00 - 4.30: Computer Lab
Wednesday May 18
09.00 - 12.00: Theory
1.00 - 4.30: Computer Lab
Thursday May 19
09.00 - 12.00: Theory
1.00 - 4.30: Computer Lab
Friday May 20
09.00 - 12.00: Theory and Guests’ Presentations
1.00 - 2:30: Computer Lab
2:30 - 4:30: Summary and Open Discussion
Content and Topics
Below is a tentative topical outline where the order of topics
may change. Contingent on availability of time, and interest,
other topics may be included and some topics may not be covered.
Morning sessions: Theory
1. Background, motivation and philosophy
- The foundations of information theory;
- What is Entropy;
- The axiomatic and combinatorial derivations
of the entropy measure;
- The basic problem;
- The classical Maximum Entropy (ME)
principle and formulation;
- The dual (concentrated) formulation;
- Basic diagnostics and test-statistics;
- Comparison with the standard ML and
other estimation methods.
2. Derivation of the basic Generalized
ME (GME) method - A simple economic example:
Recovering the unknown coefficients
of an Input-Output Table, or a Social Accounting Matrix (matrix
balancing). A complete comparison with the traditional methods
(e.g., ML) will be developed. Extensions that allow incorporating
more variables (e.g., macro/policy) and accommodating for noisy
data will be discussed in great detail.
3. The traditional linear statistical
model:
- The basic set-up of the problem;
- Basic derivation;
- Primal vs. dual formulations;
- Diagnostics.
4. A brief comparison of other information-theoretic
methods with the GME.
5. Extensions of the linear model to
non-scalar identity covariance matrix (e.g., autocorrelation,
heteroskedasticity).
6. Presentation of different theoretical
and empirical applications where the GME method is used.
7. Special additional topics (to be presented,
formulated and discussed if requested by the participants. We
can discuss all/some of these topics as well as other topics
of interest):
- Set of equations and simultaneous
equations;
- Discrete choice models (ordered/unordered);
- Censored models;
- Model and variable selection;
- Linear and non-linear dynamic systems
with control.
8. Summary and discussion of possible
future directions
Afternoon sessions: Computer Lab and “Hands on Data”
Practical examples and open discussions
will take place in the afternoons. In these sessions we:
1. will use the generalized maximum entropy
method to evaluate and estimate real world economic problems;
2. exchange/develop relevant software; and
3. discuss philosophical, practical, technical issues.
The main software package will be GAMS,
but some codes will be available in other software packages (SAS
and LIMDEP). In addition, some suggested computational problems
(and solutions) will be provided.
Target Group and Requirements
The course may be of interest to
1. PhD students interested in new methods
of estimation. Students from American University and other universities
are welcome.
2. Faculty, professional economists, researchers and econometricians
who work in support of decision making in government agencies
as well as the private market.
NOTE: Participants should have prior knowledge at the level
of an introductory course econometrics or a course in statistical
analysis (estimation techniques) at the PhD level.
Credits
The course can be taken for three credits or for no credit. To
receive the full three credits, the participant needs to complete
a research paper. Credits can only be obtained by writing the
applied paper. Students can start working on the paper at the
end of the course. The paper is due a number of weeks after the
end of the sessions (to be submitted to Golan).
Materials
- The main text is Golan, A., G.G. Judge,
and D. Miller (1996), Maximum Entropy Econometrics: Robust Estimation
with Limited Data, New York: John Wiley & Sons.
- A Reader composed of the main reading
for the class will be provided to each participant.
- A detailed reading list will be provided
with the Final Syllabus. Handouts for SAS (and LIMDEP) will
be provided as well.
Costs
Three Credit costs for students.
Fixed fee (zero credits) for Researchers.
Location
American University, Washington, D.C.
Registration
Please look at: http://www.american.edu/american/registrar/
About the instructor
Amos
Golan is a professor in the Department of Economics at American
University. He is an econometrician specialized in information
and entropy econometrics with a special interest in processing
and estimating incomplete, ill-behaved and/or non-experimental
data. His work is both on the theoretical and applied level. He
is the senior author of Maximum Entropy Econometrics, Guest Editor
for the Journal of Econometrics volumes on Information and Entropy
Econometrics and he is currently on the editorial boards of Econometric
Reviews.
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